Documentation

A type representing a Transformation for d dimensional objects

Transformations and Matrices are isomorphic.

Compose transformations (right to left)

Identity transformation; i.e. the transformation which does not change anything.

Compute the inverse transformation

>>> inverseOf $ translation (Vector2 (10.0) (5.0))
Transformation {_transformationMatrix = Matrix (Vector3 (Vector3 1.0 0.0 (-10.0)) (Vector3 0.0 1.0 (-5.0)) (Vector3 0.0 0.0 1.0))}

A class representing types that can be transformed using a transformation

Some constraints that we will pretty much need to transform a d dimensional object whose numtype is r

Bunch of constraints we need for the default implementation of transformBy

shorthand for square matrixecs

Create translation transformation from a vector.

>>> transformBy (translation $ Vector2 1 2) $ Point2 2 3
Point2 3.0 5.0

Create scaling transformation from a vector.

>>> transformBy (scaling $ Vector2 2 (-1)) $ Point2 2 3
Point2 4.0 (-3.0)

Create scaling transformation from a scalar that is applied to all dimensions.

>>> transformBy (uniformScaling 5) $ Point2 2 3
Point2 10.0 15.0
>>> uniformScaling 5 == scaling (Vector2 5 5)
True
>>> uniformScaling 5 == scaling (Vector3 5 5 5)
True

Translate a given point.

>>> translateBy (Vector2 1 2) $ Point2 2 3
Point2 3.0 5.0

Scale a given point.

>>> scaleBy (Vector2 2 (-1)) $ Point2 2 3
Point2 4.0 (-3.0)

Scale a given point uniformly in all dimensions.

>>> scaleUniformlyBy 5 $ Point2 2 3
Point2 10.0 15.0

Given three new unit-length basis vectors (u,v,w) that map to (x,y,z), construct the appropriate rotation that does this.

Euler angle rotation; in order XYZ (from bottom to top in the gimbal hierarchy)

the angles CCW and given in radians.

Rotate $alpha$-radians CCW around the x-axis

Rotate $beta$-radians CCW around the y-axis

Rotate $gamma$-radians CCW around the z-axis

Skew transformation that keeps the y-coordinates fixed and shifts the x coordinates.

Create a matrix that corresponds to a rotation by a radians counter-clockwise around the origin.

Create a matrix that corresponds to a reflection in a line through the origin which makes an angle of a radians with the positive x-asis, in counter-clockwise orientation.

Vertical reflection

Horizontal reflection

Given a box r and a geometry g with its boundingbox, transform the g to fit r.

Given a box r and a geometry g with its boundingbox, compute a transformation can fit g to r.